Astrophotography and Exposure:
What Can You Image with Various Exposures?

by Roger N. Clark

People new to astrophotography often ask what exposure does one need
for astrophotography? Here is a guide and simple method
to calculate exposure. Exposure is a combination of lens
aperture area and exposure time.

Introduction

The page shows a series of images of The Great Orion Nebula, Messier 42,
Messier 43 in the constellation Orion with increasing exposure using
a 300 mm focal length lens and a 1.6x crop DSLR. One does not need
a telescope to do a lot of astrophotography. Keys are fast lenses to
collect a lot of light and a dark site away from cities.

Exposure in terms of light from the subject is the product of lens
aperture area times exposure time. Exposure can be further refined by
including angular area. This leads to two exposure factors that I have
standardized on. 1) Clark Exposure Factor (CEF), and 2) Clark Exposure
Factor Angular area (CEFA) Further, I standardize the units: aperture
in square centimeters, exposure time in minutes, and angular area in
square arc-seconds. There are other definitions of exposure factor
(google: exposure factor photography), and other units can be used,
but my definition uses specific units for direct comparison across a
wide variety of conditions. Thus I call it the Clark Exposure Factor.
Too be clear, this is basic, well-known physics, and I only add my name
to indicate the units that I have standardized on. If you cite an exposure factor
as a CEF please be sure to use the same units: minutes and square centimeters.
If not, do not call it CEF.

Total light from the subject is key to the noise in a recorded image. The
signal-to-noise ratio is the square root of the total light received from
an object, whether daytime photography, or low light astrophotography,
and is due do Poisson counting statistics. In a perfect imaging system,
the signal-to-noise ratio we perceive in our images is the square root
of the number of photons (light) collected by the sensor, and is called
a photon-noise limited system. Other noise sources, e.g. noise from
camera electronics, or noise from light pollution, add to the photon
noise from the subject.

The basic physics is simple. For example, the light incident at
the Earth's surface from a patch of nebula, or a star, will shine so
many photons per square centimeter per minute on our telescopes/camera
lenses/eyes. For example, consider a 10 arc-second square patch of the
Orion nebula, The more square centimeters of light collection optics,
the more light is collected per minute. The more minutes of exposure,
the more total light from that patch. If two imaging systems, with
different aperture diameters were exposed with different exposure times,
the light collected from that patch would be the same if the aperture
area times exposure time are the same. Then the noise will appear the
same when the images are displayed at the same size. If they do not
appear the same, then other noise sources are influencing the result,
which may be due to noise in the camera electronics, quantum efficiency
of the sensor, or transmission of the optics. If the images were made
at different times and locations, noise from light pollution or airglow
may be contributing to the differences. Most modern lenses/telescopes
have similar and relatively high transmission. Most modern digital
camera sensors have similar quantum efficiencies (about 50 to 60%).
There is a larger range in dark currents from different sensors, and
dark current can be a large factor in the noise in an image. Noise from
dark current varies over a factor of 20 at the same temperature between
modern sensors, and over a factor of 3,000 from -10 to +30 Centigrade
when temperature effects are included. Noise from dark current is the
square root of the dark current. So choosing a low dark current camera
is important for very low light, long exposure imaging.

Below I show a series of images made with a 300 mm focal length lens.
At 300 mm focal length, combined with excellent low light high megapixel
digital cameras like the Canon 7D Mark II with 4.09 micron pixels records
fine details in many deep sky objects. A 300 mm focal length lens with
a camera with 4.1 micron pixels, resolves 2.8 arc-seconds per pixel.
It is hard to actually record more detail than about 2 arc-seconds in
long exposures due to atmospheric turbulence. Thus, it is rare that
one would need focal length longer than about 600 mm with such cameras.

Exposure, CEF

The Clark Exposure Factor is a measure of the relative amount of light received from a subject.
It can be used to fairly compare wildly different lens/telescope apertures and exposure times.

Astrophotos made with the same CEF regardless of aperture and exposure time will be similar
in image quality when made with approximately the same focal length (close to the couple
of arc-seconds per pixel) and presented at similar sizes.

Exposure, CEFA

For widely varying focal lengths where you want to record a similar light density, include the
pixel angular area. This is CEFA:

Clark Exposure Factor Angular area, CEFA = aperture area in square centimeters * exposure times in minutes
times angular area in arc-seconds.CEFA = (pi/4) * (aperture diameter in cm)2 * time in minutes * angular area in sq. arc-seconds

The first step is to determine the angular size of a pixel, called the plate scale.
See Plate Scale for details on the equations and
tables for cameras and focal lengths.

The pixel angular area is the square of the plate scale, 2.8*2.8 = 7.8 square arc-seconds.

For example, the CEFA for the image in Figure 1 is the CEF * pixel angular area
= 1.5 * 7.8 = 11.7 minutes-cm2-arc-seconds2.

Why is CEFA important? Say you saw the image in Figure 1, but wanted
to make a higher resolution image on a night of very steady atmosphere,
with imaging at 1-arc-second per pixel and a 150 mm diameter lens.
What exposure time would you need to get the same signal-to-noise ratio
per pixel? The image in Figure 1 has a 1/60 second
exposure time, so the CEFA with the 150 mm (15 cm) diameter lens in 1-second would be:
CEFA = (pi/4) *152 * (1/60 minutes) * 1 sq arc-second = 2.95 minutes-cm2-arc-seconds2.

The images were made with daylight color balance. This is a stock
camera with very close spectral response similar to the human eye.
Astrophotographers often modify cameras for increased sensitivity to
Hydrogen-alpha emission (red). The pink and light blue colors are
close to what I have seen visually through large telescopes though a
little more pastel. Hydrogen emission nebulae actually appear pink
due to H-alpha (red), H-beta (blue) and emission from other atoms,
like oxygen and sulfur. Modified cameras over emphasize H-alpha, making
hydrogen emission nebulae come out red in photos. Unmodified cameras
do a better job at color separation of the various processes that occur
in the deep sky. Modified cameras tend to show mostly red in areas
like that in this image, making it too difficult to tell the difference
between dust and hydrogen emission nebulae. See Parts 2a - 2d of this
series for descriptions of the natural colors in the night sky

Figure 1. Full resolution image of the Trapezium region of M42, 1 second
exposure. This image shows the teal color of the Trapezium. This is
the color I see in large amateur telescopes when observing the Trapezium.
Image at full resolution.CEF = 1.5 minutes-cm2.CEFA = 11.7 minutes-cm2-arc-seconds2.

Figure 4. M42, nine 1-minutes exposures averaged. Each image was like the one in Figure 3, and
does include the image from Figure 3 in the average. As more images are added together, the signal-to-noise ratio
improves, more faint details can be brought out and more details in brighter areas shown.
This image is 1/3 of full resolution.CEF = 810 minutes-cm2.CEFA = 6350 minutes-cm2-arc-seconds2.

Sub-Exposure Length

The above exposure series used shorter exposures averaged together to achieve
a given total integration time. To achieve detection of very faint light
from stars, galaxies, nebulae, comets and other faint things in the night sky, one must
minimize noise sources. The noise sources include:

Photon Noise from the subject itself (square root of the total photons collected from the subject),

Photon Noise from light pollution and airglow (square root of the total photons collected from the sky),

Photon Noise from the sensor and downstream electronics (apparent read noise), and

Photon Noise from dark current (square root of the thermally generated electrons in the sensor).

Other factors also reduce efficiency when sub-exposures are short:

Inter-frame delay: the time to record and image and start the next frame,

More readouts could heat the sensor, increasing dark current.

In making long exposures, the goal is to achieve a reasonable
signal-to-noise ratio (S/N) and a sharp image. We can do that by using a large aperture
lens/telescope. Noise from light pollution will be less if the light
pollution is small, and you can make that happen by traveling far from
cities, or use filters to block at least some of the light pollution
(note that also blocks some light from the subject). Apparent read noise
is a characteristic of a given camera. Apparent read noise generally decreases with
increasing ISOs. Internet "experts" are generally obsessed with read noise,
but it is relatively simple to make it insignificant by simply doing
long enough exposures. Dark current noise is a function of temperature
and generally doubles for every 5 to 6 degrees C increase in temperature.
The only way to improve noise from dark current is to image on a cold night, do active cooling,
or choose a camera with lower read noise (or all of these things).

To minimize the effects of read noise, simply expose long enough to get the histogram
peak at about the 1/4 to 1/3 level on the camera LCD (Figure 6). Try and avoid
the histogram peak going above the half way point as dynamic range can be impacted.
This guideline works for read noise in the 2 to 4 electron range, which applies
to most recent model digital cameras when used at ISOs around 1600.
For lower read noise values, e.g. 1 to 2 electrons, lower histogram levels
can be used without detrimental effects. More specifics are given below.

The histogram is a variable gamma scale and the 1/3 point means a signal
at about 3% of full scale for the sensor. So if the sensor has a range of 2000 electrons
maximum signal, that means the sky in the 1/4 to 1/3 histogram range would be
about 60 electrons in that exposure, whatever length it might be. As you may surmise,
with typical read noise below 3 electrons for modern digital cameras, the noise from the
sky is much greater than the sensor apparent read noise (square root 60 =
7.7 which is obviously a greater number than 3. Some internet
"experts" don't seem to understand this). So just keep your exposures
long enough to get the histogram at the 1/4 to 1/3 level and you've done
a good job of minimizing read noise contributions. What is more important is total exposure time.
Once sub-exposure time reaches the 1/4 to 1/3 histogram level, longer sub exposure will not
help, given the same long exposure time. Table 1 gives a guideline for dark site to very light polluted sites.

Figure 6. Histogram of a night sky image. The blue channel peak is at
about the 1/3 of the distance from the left to the right edge.

The above discussion argues for longer sub-exposure times.
But there are factors that limit the length of sub-exposure times. These include:

Seeing limitations,

Wind gusts,

Stable Tracking limitations, and

Airplanes and Satellites contaminating the field.

Seeing is the bouncing around and blurring of the image due to atmospheric
turbulence. The atmosphere may be stable for short periods, but then
degrade with heat waves in the atmosphere between your camera and
outer space. Shorter exposures can be selected to use only the images made in
the most stable atmosphere periods. Random wind gusts can shake the
imaging setup, moving the image around in the scene during exposures,
burring the recorded image. The shorter the exposure, the higher the
probably the exposure will complete before another wind gust. Tracking
systems have periodic error and if you are not using an autoguider
to correct this or you have slower drifts from polar alignment errors or drive
rate errors, you are limited as to how long you can image before drift
impacts image quality. Airplanes and satellites going through the image
can be rejected using sigma-clipped averages if you have many frames
to combine. If you have only a few frames, rejection of airplane and
satellite trails are not well rejected and you must simply throw them
out losing efficiency (or tediously clone them out after the stack).
Try for at least 10 frames to combine (see Part 3e, Image Processing:
Stacking Methods Compared) for methods to combine a set of images.

Figure 7. An imaging sequence with a 300 mm lens on the Lagoon Nebula.
These images are crops at full resolution and 2.8 arc-seconds per pixel.
Thirty eight 1-minute exposures were obtained and I produced the image
on the left using all the frames. But examining the individual frames
showed many had terrible seeing, or shakes from wind (although I remember
it being very calm night). Rejecting the worst of the sequence left
me with half the number of sub-frames (right panel). Clearly the right
panel with half the frames produces a sharper image. The image on the
left has halos around the stars, artifacts in processing trying to make
smaller star images. The artifacts are smaller, if there are any at all,
in the image on the right. The image on the right is aesthetically
better, records fainter stars and finer detail with only half the
total exposure time. The higher contrast in the finest details meant
less stretching so the lower signal-to-noise ratio is not detrimental.

Putting the above concepts together on dropping efficiency as sub-exposure
length decreases, to lower efficiency as exposure times become longer
due to seeing, wind, tracking, and interference from satellites and
aircraft we get efficiency plots like that shown in Figures 8a, 8b, 8c. Even if
your system has an autoguider and tracks perfectly, the other factors,
like seeing still affect the final result.

Figure 8a. Sub-exposure efficiency model.
The model assumes the same total integration time + interframe delay time.
For example, what sub exposure time produces the best signal-to-noise ratio
in 240 minutes of actual time?
These are the typical parameters for a camera
like a Canon 7D Mark II and seeing limited tracking of a large lens with
plate scales of 3 arc-seconds per pixel and smaller.
Note, the object signal is very faint for this case: 1/10th the signal from the sky,
a worst case scenario.

Use these spreadsheets to tune the model for your systems and environmental
conditions. The spreadsheets were created with libreoffice on linux, and I have
tested both on a windows excel program. The xls file is probably best to use with
windows and excel.

In using the model, you can look up the read noise and dark current for your
camera, e.g. here.
If you can't find dark current for your camera, estimate it from
the blue and cyan lines in
Figure 3 here. For the exposure time stability, first determine
your total desired exposure time, say it is 100 minutes. Divide that by
(approximately) 10 so that you have many sub-frames to stack and reject
satellites and airplane tracks. That is the maximum sub-exposure time
to consider. Next, what is the longest your mount can track a subject
when you would reject a frame 50% of the time. If this is shorter than
the minimum number of frames calculation, use this new number. Next is
to evaluate environmental conditions: how long between wind gusts, and
how long is the seeing stable? Use the shortest time from all these
factors for the Exposer Time Stability factor.

The above model and example in Figure 7 clearly demonstrates that
tuning sub-exposure length to best work with limitations of the system
and environment can result in a better final image. Also Figure 7
illustrates that there are important factors in producing astrophotos
than simply accumulating maximum exposure time. This means limiting
sub-exposure length when seeing, wind, and tracking limits image quality
and reject frames that are not sharp. If you end up rejecting many
frames, that is reducing efficiency and in your next session, try shorter
sub-exposure times.

Figure 8b shows model results for an older camera used at low ISO. The high
read noise shifts peak efficiency to longer wavelengths. But note the
efficiency is actually lower than with the lower read noise camera using shorter
sub-exposures as shown in Figures 8a and 8c!

Some cameras are now in the 1-electron read noise range. Compared to the
results in Figure 8a, we see the peak efficiency of the 1-electron read
noise camera is shifted shorter to less than 1 minute. When sub-exposure
times approach and become shorter than about a minute, the inter-frame
delay to write results to the memory card become the major factor
in efficiency. Use fast memory cards and reduce the delay time to the
minimum. Be sure that the write cycle completes before the next exposure
starts because the higher electronics activity can add noise to the next
image if the camera is writing results during an exposure. For a Canon
7D Mark II, I use a 2-second delay for writing the image to a fast card,
and 2-second mirror lock up delay, for an inter-frame delay of 4-seconds.

Figure 8b. A high read-noise, high dark current sensor, typical
of older cameras or using low ISO on some older cameras
with the same observing conditions as in
Figure 8b shows that the efficiency drops and the peak efficiency moves
toward longer exposure times, but only by a small amount.
The read noise is typical of a Canon 5D Mark III at ISO 400.

Figure 8c. A very low read-noise sensor with the same observing conditions
as in Figure 8a. Peak exposure time is slightly less than 1 minute.
Efficiency could be improved by reducing the inter-frame delay by using
memory cards that write the image faster. Reducing the delay moves the
peak efficiency to shorter exposure times.

The above model in Figure 8a uses better seeing than in the M8 images
in Figure 7. In practice for the M8 image, I should have used even
shorter exposure times than 1 minute. By selecting only 19 of 38 (50%),
the efficiency was (use the yellow curve, Figure 8a: 90% at 1 minute)
0.9 * 0.5 = 0.45, or 45% with 1-minute sub exposure, and longer times
would have been worse. Changing the stability to 1 minute, increasing
ISO to 3200 where read noise is 1.9 electrons (Figure 8c), the peak
efficiency exposure time would be about 30 seconds and I would have
achieved a 58% efficiency (29% better than with 1-minute subs). Again,
low efficiency is not a horrible issue if it leads to a better final
image, and neither are short sub-exposure times.

Figure 8d. Model for the conditions with the M8 image sequence in
Figure 7 where 50% of exposures get rejected with 1-minute sub-exposures.
I should have used 30 second exposures at ISO 3200.

Technical.
You can estimate the photons from the sky relatively simply for any
modern camera. The maximum signal at base ISO for silicon photodiode
sensors (that means CCDs and CMOS sensors in digital cameras) is about
2100 electrons per square micron. For example, the images above were
made with a Canon 7D Mark II at ISO 1600 with 4.09 micron pixels, so
it will have 2100 * 4.092/16 = 2200 electrons (ISO 1600).
The 1/3 histogram level on the camera LCD (which is a log scale, or
more precisely a variable-gamma scale) is at abut the 3% of full scale,
or about 66 electrons. The 1/4 histogram level is about 2% (2.2%)
of full scale or about 48 electrons in this example. So by a simple
glance at the histogram on the camera LCD, one can make a quantitative
estimate of the signal level in electrons in the image, and thus, photons
from the sky). More specifically, for signals less than about 40%
of max signal in the tone curve data, e.g. jpeg output, the electron
count can be measured by the formula:

where DN = the image Data Number, 0 to 255, and P is the maximum signal
in electrons in a pixel at the ISO used. For example, the frames used
to make the M42 images, Figures 1-5, had a sky level of about 60 DN. The 7D2
has a max signal of 2230 electrons at ISO 1600, so the sky level was
2230 * 60 / 2550 = 52 electrons.

If you adhere to the 1/4 to 1/3 guideline for exposure time per image. you
will always get a fixed signal from the sky and know that read noise is
an insignificant contributor to the image. Of course, as sky brightens
from light pollution, airglow, aurora, or twilight, exposure times per
frame will need to be reduced (Table 1), and the noise from the sky will
become a greater and greater impact on the signal-to-noise ratio you can
achieve in the final astrophoto.

The 1/4 to 1/3 histogram guideline applies to cameras with read
noise in the 2 to 4 electron range (common values for modern digital
cameras; good cameras newer than circa 2012). As read noise decreases,
the histogram level can be reduced. If read noise were zero, it would
not matter what exposure time one used (even video rates), assuming the
same total exposure time. For cameras with ~1 to ~2 electron read noise,
the exposure times in Table 1 can be reduced (e.g. 1/10 to 1/5 histogram
level with little impact on noise in the final image.

Technical Example to Show Sub-Exposure Time Effects on Total Noise.
The images on this page were made on a night of high airglow in a
blue/green zone.
The measured sky level, as described above was 52 electrons per
1-minute exposure (24% histogram level). Dark current was 0.02
electron/pixel/second, or 1.2 electron per minute. Read noise was 2.4
electrons. For a signal of 10 photons per minute, what signal-to-noise
ratio (S/N) would be achieved?

S/N = S * n /sqrt(n * ( S + a + r^2 + d)), (equation 2)

Where S = the signal (10 photons per minute) from the object (after sky
is subtracted), n =the number of sub exposure frames averaged, a = signal
from airglow and light pollution, r = red noise and d = dark current).
Plugging in the numbers above, we get the S/N for various exposure times
added to make 28 minutes total exposure time.

From Table 2, we see the impact of read noise is minimal with only
about a 5% loss with short exposure times of 30 seconds to a minute.
It would be hard to tell the difference between a sensor with zero
read noise, or with a single 28-minute exposure versus 28 one-minute
exposures averaged. I wrote this up because the internet "experts"
were at it again, attacking me saying I need to do longer sub exposures.
The concepts of needing long exposure times dates to old technology when
sensor read noise was higher than 10 electrons, but this is no longer
true with modern sensors.

When read noise gets lower than 1 electron, one could do video and
stack video frames and still make amazing images. In fact, then one
could do lucky imaging and improve resolution, like that done with
planetary imaging.

Advantages and Disadvantages of Short Exposures

Short exposures have the following advantages assuming the same total
exposure time as frames are averaged (stacked):

Can track moving objects in post processing (e.g. comets against the star background).

Little loss of integration time when a frame must be rejected (e.g. from someone
turning on a light, bad seeing, wind gust, or bumping the system).

Disadvantages of short exposures:

More data to process and store,

Potentially increased image noise in the final stack if read noise becomes large
relative to noise from the sky and dark current
(see Figure 8 and the efficiency model spreadsheets above).

Light Pollution Effects

Light pollution increases noise, thus read noise becomes even less
important as light pollution increases. But for every doubling of light
pollution intensity, to record that same faint objects, you need 4 times
the total exposure. Following on the concepts first introduced above,
CEF and CEFA, there are 3 ways to improve exposure: increase
aperture, increase exposure time, and for CEFA, increase angular area of a pixel.

The simple way to increase angular area is by averaging pixels together
(binning). Note f/ratio does not come in to play in the equations.
Another way to lower noise from light pollution is to block it from the
sensor by using a light pollution filter (this will be the subject of a
future article and not discussed here).

When light pollution is high, exposure times must be shorter than from
a dark site, but that leads to many short exposures to manage. So one
way is to spread that light over more pixels. The above images were made
with a 300 mm f/2.8 lens. From a red zone, exposure times would need to
be just a few seconds to keep the histogram peak from getting too high.
One could add a 2x teleconverter to spread the light out (it is the same
amount of light from the object and sky, just spread over more pixels
(also, this assumes the object still fits in the frame). That enables
4 times longer exposure time, collecting more light per exposure and
reducing sub-exposure count by 4. Then in post processing, bin the
pixels 2x2, 3x3 or even 4x4 to improve S/N. You still need more total
integration time than from a dark site to deal with the increased noise
from the light pollution, but the frame count is more manageable, and by
binning you need less total exposure time than would be needed without
the teleconverter.

Binning directly increases dynamic range, increases maximum signal, and
increases S/N by the bin factor. A 2x2 bin improves S/N, maximum signal,
and dynamic range by 2 times. A 3x3 bin improves S/N, maximum signal,
and dynamic range by 3 times. It is effectively making an increase
in pixel size with a corresponding loss in resolution, just as if you
were imaging with a camera with larger pixels. With low noise cameras
and where sky glow is higher than read noise there is effectively no
difference in binning in post processing versus binning on the sensor
(which is available in some CCDs). Binning is also effectively lowering
the ISO by the bin factor and increasing the digitization bits by the bin
factor with none of the detrimental effects of lowing ISO, so no increase
in noise from downstream electronics. A 2x2 bin effectively increases
the bit depth in a 14-bit camera to 16 bites, a 3x3 bin to 16 bits.

For example, the red zone data for f/2.8 from Table 1 indicates exposures
of about 10 seconds to get to the 30% histogram level. Stretch that to
about half histogram level (20 seconds at f/2.8), add the 2x teleconverter
and you get 80 second exposures (f/5.6). That puts one in the ballpark
for short exposures at a dark site. The noise from the light pollution
is still there, so you still need to expose several times longer than
at the dark site to reach the same faintness, but it makes the problem
a little more plausible. Bin 2x2 to get the same resolution as imaging
without the teleconverter and you are imaging with a lower noise higher
dynamic range and higher bit depth system. It is these characteristics
that mitigate light pollution effects.

Technical. Following on equation 2 above, the signal measured,
M, is the intensity, S, from an object in the night sky plus pollution,
a, in a single exposure.

M = (S + a), (equation 3a)

N = sqrt(S + a + r^2 + d), (equation 3b)

We want to subtract the sky brightness from M to get S, the signal from the
astronomical object. S = M - a

So we subtract the amplitude of the sky brightness in equation 3a, but the
noise remains unchanged (equation 3b still applies). The Noise
has not changed, contrary to some internet "experts." But because
the signal from the astronomical object, S, is less than M, the S/N
decreases as the light pollution increases (the value of "a" in equation
3b increases). Because "a" can get very large in big cities, light
pollution is detrimental to photographing dim astronomical objects.
The only solution to maintaining the signal-to-noise ratio, as light
pollution increases, is longer total integration time. Because "a" gets
larger than the other components in the noise equation 3b, noise in
the final astrophoto increases as the square root of the light pollution,
and to recover that S/N, the exposure time must be increased as the
square of the increase in light pollution.

Example images with effects of light pollution are shown in Figures 9a ad 9b.
The images were made in a red zone, green zone and at a very dark site (dark gray zones
on light pollution maps) and processed to produce the best image I could.
All were made with the same 107 mm diameter lens. The red and green zone
images were made with a Canon 7D mark 1 with 4.3 micron pixels. The dark zone image
was made with a 7D Mark 2 with 4.09 micron pixels which has a better sensor, but the
main effects shows here are dominated by effects from light pollution.

Compare the images in Figure 9a and 9b. In 9a, the light pollution was extremely
bright, even with the light pollution rejection filter used. The high light pollution,
which was subtracted, meant difficulty in establishing a very uniform background,
leading to the red-blue splotchiness seen in Figure 9b, left panel. The dark
site, which had some airglow that needed to be subtracted, produced
a much smoother and more uniform color. I had to spend a lot more time on the
red zone image to subtract the background and control color balance.
Images made through the IDAS LPS-P2 filter come out very blue with daylight
white balance. In the raw converter, one can set a custom white balance
of about 7600 Kelvin with tint in ACR around +35. Those setting gave a
relative neutral color to solar-type stars in my case.

Figure 9a. Comparison of best effort processing for M31 images made
in red zone light pollution, green zone light pollution, and at a very dark site.
Seeing for the dark site was better than the other 2, resulting in smaller star
images. Sub-exposures were 60 seconds for all three cases.
The most natural color is the image from the dark site.
Dark site M31 gallery image with more details.

Figure 9b. Comparison of best effort processing for M31 images made
in red zone light pollution, and at a very dark site. The left image
is at full resolution, being made with a Canon 7D mark 1 camera.
The right image is downsampled to the same scale as the 7D1 image.
The right side image was made with a 7D Mark 2 camera, and although
a better sensor, the major differences shown here are due to
the effects of light pollution.
Dark site M31 gallery image with more details.

Discussion and Conclusions

By examining the CEF and CEFA values for the various exposures, some
general guidelines can be derived. I base this not only on these
images, but the many other astrophotos that I have made with recent
model digital cameras.

First, for plate scales in the couple of arc-seconds per pixel range,
which matches typical resolution limited by atmospheric turbulence
(seeing), CEF values 100 to few hundred range will get to levels that can
be seen visually in large telescopes from dark sites. These levels can be
achieved from sites 30 to 50 miles from the center of large metropolitan
centers of a 2 to 3 million people (green to blue zones on light pollution
maps). CEF values in the 1000+ range improves signal-to-noise ratio
and brings fainter subjects into view. I strive for CEF in the 2000 to
3000 range, though 300 to 4000 is better. Some very faint nebulae and
galaxies can benefit from CEF levels of 6000 or more.

When comparing diverse resolution imaging, use CEFA. CEFA in the 700+
range records levels that can be observed visually in large amateur
telescopes. But 10,000 to 20,000 is needed to image faint objects in
high resolution.

For example, images made with a 35 mm f/1.4 lens on a camera with
5.7 micron pixels and 30 second exposures have CEF = 2.45 With 33.6
arc-seconds per pixel, CEFA = 2770, so a little better than the CEFA
in Figure 3. But a nightscape made with a 15 mm f/2.8 lens, 30 second
exposure would only have a CEF = 0.11, 78.4 arc-seconds per pixel, and
CEFA = 693. This says the 35 mm f/1.4 lens will record significantly
fainter details.

The CEF and CEFA indicators above are based on reasonably dark skies,
blue and green zones on light pollution maps. For sites with more light
pollution, additional exposure is needed. In general, for every doubling
of sky brightness, exposure factors must increase about 4 times to reach
the same faintness.

Credible images can be made in areas of strong light pollution, however,
it is difficult to get as faint, it takes more processing to subtract
the light pollution well and it can be difficult maintaining a good
color balance. The extreme stretched needed in high light pollution
environments result in magnification of camera non-uniformities, further
degrading the final image quality. Obviously, image quality improves
with dark sites with less light pollution, but with careful processing,
one can record somewhat faint objects in the night sky even in areas of
strong light pollution.

There are other factors than simply exposure time in producing a detailed,
low artifact astrophoto. Choosing sub-exposure length for good efficiency,
yet allowing one to reject periods of bad seeing, wind gusts, tracking errors,
or bumping the system is more important than simply stacking every frame
measured in an effort to maximize signal-to-noise ratio. In other words,
bad data in, bad data out. Don't let a few exposures with bad image quality
contaminate many high quality images in order to maximize signal-to-noise ratio.

Finally, be wary of internet "experts" who say you need to expose for
hours to get great images. Gee, people made great images on film with an
hour or so exposure time, and film is 20 and more times less sensitive
than modern digital cameras! It didn't take days to get great images
on film, and it doesn't take hours with digital cameras. The metric,
as we have seen above, is not simply exposure time.
It is CEF and CEFA.
Also, be wary of internet "experts" who say your sub-exposure times are
too short and you would do better with longer sub exposures, especially
when your exposure times are in a good region of the sub-exposure
efficiency model above.

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